<span>We want to optimize f(x,y,z)=x^2 y^2 z^2, subject to g(x,y,z) = x^2 + y^2 + z^2 = 289.
Then, ∇f = λ∇g ==> <2xy^2 z^2, 2x^2 yz^2, 2x^2 y^2 z> = λ<2x, 2y, 2z>.
Equating like entries:
xy^2 z^2 = λx
x^2 yz^2 = λy
x^2 y^2 z = λz.
Hence, x^2 y^2 z^2 = λx^2 = λy^2 = λz^2.
(i) If λ = 0, then at least one of x, y, z is 0, and thus f(x,y,z) = 0 <---Minimum
(Note that there are infinitely many such points.)
(f being a perfect square implies that this has to be the minimum.)
(ii) Otherwise, we have x^2 = y^2 = z^2.
Substituting this into g yields 3x^2 = 289 ==> x = ±17/√3.
This yields eight critical points (all signage possibilities)
(x, y, z) = (±17/√3, ±17/√3, ±17/√3), and
f(±17/√3, ±17/√3, ±17/√3) = (289/3)^3 <----Maximum
I hope this helps! </span><span>
</span>
Answer:
$25 I believe
Step-by-step explanation:
You would take $37.50 divided by 3 and get $12.50 which is the price of 1 ticket
Then you would multiply $12.50 x 2 to get $25
The weight of the third heaviest among the four dogs is 2 kg.
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more numbers and variables.
The 4 dogs weight is 60 kg with each dog weight been different. The second heaviest dog weighs 28 kg.
Let the heaviest dog be 29 kg, the third heaviest be 2 kg and the fourth be 1 kg.
29 + 28 + 2 + 1 = 60 kg
The weight of the third heaviest among the four dogs is 2 kg.
Find out more on equation at: brainly.com/question/2972832
Answer: I do not age
Step-by-step explanation: I have magical Phoenix powers and i drink a lot of ageless potions
